1998 Mercury Sable failure to turn over or start

Hello, I am trying to assist my mother w/ a recurrent problem: the car will not turn over or start at times. This has happened 3-5 time in the last 9-12 months, for no apparent reason. A couple of time the weather was hot, so I suspected tghe engine was overheated. A couple of other times, though, temps were not high and car hadn't bee driven very far. Could just be idling at a light, or car was turned off for a time & just won't restart. If it sits untouched for 45 mins. To an hour, will then start and run fine for indefinite period, w/ no signs of a proble, until the next (random & unexpected) instance./ She's had it on dignostic machine twice, and they cannot identifly the cause. If you have any suggestions or solution to this perplexing problem, we would really appreciate your help. Thanks! Phil